I own a copy of that book, and I also highly recommend it! (The full title is "Physics for Mathematicians: Mechanics I", but sadly we're now never going to get a "Mechanics II".) It has a different goal than my notes --- he's more interested in building up classical mechanics very, very carefully from first principles --- but it's a fun journey if you have the time to spend on it.
As a former physicist, I never understood the full math behind Schrodinger's equation. Since then I ventured into CS, so I wonder if this book will be a good refreshment.
The Schrodinger equation is just restating something you may already know if you studied physics. The Hamiltonian is the generator of time translations.
https://archive.org/details/physics-for-mathematicians-mecha...
It's a very interesting take on classical mechanics.